Contour plots use lines or colors to represent three-dimensional data on a flat surface. Each line connects points that share the same value, whether that value is elevation, temperature, air pressure, or a mathematical function. Once you understand a few core principles, you can read contour plots in any field, from hiking maps to scientific data visualizations.
The Basic Rule: Lines Connect Equal Values
Every contour line traces a path through points of identical value. On a topographic map, a line labeled “500” connects every point at 500 feet of elevation. On a weather map, a line labeled “1016” connects every point where atmospheric pressure is 1016 millibars. The specific quantity changes depending on the plot, but the principle never does.
The spacing between adjacent lines is called the contour interval, and it’s the single most important number on any contour plot. On a topographic map, a contour interval of 20 feet means each line represents a 20-foot change in elevation from the previous one. The U.S. Geological Survey uses intervals as small as 10 feet for flat terrain and 100 feet or more for steep mountain areas. The contour interval is always printed somewhere in the map’s margins or legend, so check it before interpreting anything else.
What Line Spacing Tells You
The distance between contour lines reveals how quickly values are changing. Lines packed tightly together mean the value is changing rapidly over a short distance. Lines spread far apart mean the change is gradual. On a topographic map, tightly spaced lines indicate a steep cliff or hillside, while widely spaced lines indicate flat or gently rolling ground. This same logic applies everywhere: on a weather map, tightly packed pressure lines (called isobars) mean a strong pressure gradient and fast winds, while loosely spaced isobars mean calm conditions.
Think of it this way. If you have to climb 200 feet of elevation and the contour lines are crammed into a tiny horizontal distance on the map, you’re looking at a near-vertical slope. If those same 200 feet of gain are spread across a wide area, you’re looking at a gentle hill.
Reading Peaks, Valleys, and Depressions
Closed loops on a contour plot mark either a peak or a pit. If the values increase as you move toward the center of the loops, you’re looking at a peak (a hilltop on a terrain map, or a local maximum in a math plot). If the values decrease toward the center, it’s a depression or pit.
On topographic maps, depressions get a special visual marker: small tick marks called hachures that point inward from the contour line toward lower ground. Without hachures, closed contour loops represent high points. With hachures, they represent low points like craters or sinkholes.
A saddle point appears where two peaks sit near each other with a dip between them. On a contour plot, you’ll see an hourglass-like pattern: closed loops on either side (the peaks) with a gap of lower values running between them. In mathematics, saddle points are spots where the value rises in one direction but falls in the perpendicular direction, creating a shape like a horse saddle or the center of a Pringle chip.
Recognizing Terrain Features by Shape
If you’re reading a topographic map, specific contour shapes correspond to recognizable landforms. A ridge appears as a long stretch of high ground where contour lines form elongated, roughly parallel curves. Every point along the ridge crest is higher than the ground on either side. A spur is a shorter tongue of high ground that juts out from a ridge, like a finger extending from a hand.
Valleys show up as U-shaped contour lines that tend to run parallel to a stream before crossing it. Here’s a useful trick: where contour lines cross a stream or river, the lines always point upstream. So the V or U shape formed by the contour lines points toward higher ground and the water’s source. This is sometimes called the “rule of Vs.”
How To Read Filled Contour Plots
Many scientific and engineering plots replace individual lines with bands of color, creating what’s called a filled contour plot. Instead of reading line labels, you read a color scale (usually printed alongside the plot) to determine what value each color represents.
Two types of color scales dominate. Sequential scales run from dark to light (or light to dark) and represent a single quantity that increases in one direction, like surface height, temperature, or chemical concentration. The key feature of a good sequential scale is that it has an obvious direction: darker means less, lighter means more, or vice versa. If you can’t immediately tell which end of the scale is “high,” the color choice is poor.
Diverging scales use two contrasting colors that radiate outward from a neutral midpoint, typically representing deviation from some average or zero value. Red for positive and blue for negative is the most common convention. If you see a plot where warm and cool tones meet at a neutral center color, you’re looking at diverging data, and the midpoint matters as much as the extremes.
Be cautious with rainbow color scales (sometimes called “jet” scales). They look vivid, but they aren’t perceptually uniform. Certain colors in the rainbow appear brighter than others, which tricks your eye into seeing sharp boundaries where the data actually changes smoothly. A band of yellow, for instance, can seem to “pop” compared to neighboring greens and oranges, making that value range look more important than it really is. Sequential or diverging scales are more reliable for accurate interpretation.
Reading Contour Plots in Math and Science
In mathematics, contour plots visualize functions of two variables. The x-axis and y-axis represent the two input variables, and the contour lines show the output value. Finding a local maximum means looking for a set of closed loops where values increase toward the center, like a bullseye. A local minimum is the same pattern but with values decreasing toward the center.
Saddle points in math plots are trickier. They look like a spot where contour lines from two different “peaks” nearly meet but bend away from each other. If you mentally slice through the saddle in one direction, values go up (like a minimum turning into an increase). Slice perpendicular to that, and values go down (like a maximum turning into a decrease). The contour lines near a saddle point often form a pattern resembling a figure-eight or two sets of curves turning away from each other.
The same line-spacing rule applies here: tightly packed contour lines mean the function’s value is changing steeply, while widely spaced lines indicate a flat region where the output barely changes.
Practical Tips for Any Contour Plot
- Check the legend first. Identify the contour interval or color scale before looking at the plot itself. Without knowing the interval, you can’t determine actual values or rates of change.
- Contour lines never cross. A single point can’t have two different elevations or values. If lines appear to cross, look more carefully: one is likely a different type of line (like a trail or boundary) overlaid on the map.
- Count lines between labeled ones. Most maps only label every fourth or fifth contour line (these thicker lines are called index contours). To find the value of an unlabeled line, count how many lines sit between two labeled ones and divide the difference by that count plus one.
- Interpolate between lines. If you need the value at a point that falls between two contour lines, estimate based on how close the point is to each line. A point sitting halfway between the 400 and 420 lines is roughly at 410.
- Look at the big picture first. Before zooming into details, scan the whole plot to find the highest values, lowest values, steepest gradients, and flattest zones. This gives you the overall structure before you start reading specific features.